In the right triangle shown, $AC = 8$ and $BC = 4$. What is $AB$ ? $A$ $C$ $B$ $8$ $4$ $?$
Solution: We know $a^2 + b^2 = c^2$ We want to find $c$ ; let $a = 4$ and $b = 8$ So $c^2 = 4^2 + 8^2 = 80$ Then, $c = \sqrt{80}$ Simplifying the radical gives $c = 4\sqrt{5}.$